Multi-layer polymeric structures are suitable for flexible and for rigid packages for food. Flexible multi-layer films are used for pouches, bags, and wraps. Thicker multi-layer structures can be formed into containers in the shapes and sizes common for metal cans. Sufficient impermeability to oxygen throughout the expected storage life of the packaged product is a necessity. Most economically practical polymers suitable for packaging purposes are relatively poor oxygen barriers. Consequently, an interior layer of a polymer impermeable to oxygen is desired. Among the favored candidate polymers for barrier layers are ethylene-vinyl alcohol (EVOH) and polyvinyl alcohol (PVOH). Both are excellent oxygen barriers, but both are quite moisture sensitive. Above a relatively modest moisture content, both rapidly begin to lose oxygen barrier quality. There are several opportunities for intrusion of moisture into the barrier layer from the packaged food itself, from storage in moist air and from water vapor present in commercial sterilization processes.